We give a description of the binary cold fission process of ²⁵²Cf within the stationary scattering formalism. The decay of the dinuclear system (quasi-molecule) consists in the tunnelling of a metastable state from an internal region, where the nucleus–nucleus potential makes a quasi-molecular pocket due to the interplay of repulsive and attractive nuclear forces and the Coulomb force, to the asymptotic region which is governed solely by the Coulomb repulsion. As a transverse internal motion, we suppose angular oscillations of the fragments up to the scission point. In the external region these vibrations transform into rotations. The nuclear interaction is given by a double-folding procedure using M3Y forces plus a repulsive contact potential. For the experimental Q-value we find several resonant states of the binary system, depending on the repulsive strength. We predict a strong dependence of decay widths upon the internal structure of the considered resonant state. Therefore the measured yields of the two fragments with given angular momenta in coincidence are able to provide more insight into the internal molecular dynamics of the decaying dinuclear system.